### Further Reading

# Overview: Three models of light

#### Prerequisites

## A brief history of the theories of light

To anyone interested in our interaction with the physical world, the question, "How do we see?" has got to be pre-eminent. Lots of the information we've garnered about the world comes from seeing, so to make sense of our making sense of the world, we need to figure out how seeing works.

There are really two parts to this question:

- What is it that brings information to us from the outside world?
- How do we take that information and convert it to an understanding of what's out there.

While the second question is definitely the purview of biologists (and particularly their subfields of neuroscience, cognitive science, and psychology), the first falls firmly in the field of physics.

In the early days of documented exploration of the character of the world we live in, the Greeks proposed *the emission theory* that assumed that light was a substance that came out of the eyes. Euclid stated that light traveled in straight lines and knew the law of reflection. Refraction was described by Ptolemy nearly two thousand years ago. Aristotle thought that vision arose because something came to the eyes.

About the year ninth and tenth centuries, Arab natural philosophers made a convincing case against the emission theory and made many developments and treated light as projectiles.

The next great advances came in the 17^{th} century with the work of Newton and Huygens. Isaac Newton took the particle model of the Arabs (and of Gassendi) and created a robust model of light that could be calculated mathematically — the ray model. At about the same time, his oft-times competitor, Christian Huygens, developed a model of light as waves propagated through a material that filled the vacuum — the "ether".

At the beginning of the 18^{th} century, the wave theory began to be increasingly the only way to explain more and more data about light and was the dominant model for most of the century. In 1865, James Clerk Maxwell proposed a theory that unified electricity and magnetism and predicted that light was in fact a wave of oscillating electric and magnetic fields. Running with this idea, Hertz in the 1880's demonstrated that the theory worked by generating radio waves. Radio, television, radar, and wifi followed.

But towards the end of the 19th century, as scientists were beginning to figure out that matter was made up of atoms and what their nature was, the prevailing theories encountered some contradictions. In the early 20th century, led by Einstein, physicists developed a hybrid model — photons — that treated light as made up of particles with wave characteristics. (Wait....What?) These "wavicles" display all the weirdness of quantum physics and that "quantum weirdness" is currently being used and worked with to demonstrate how truly weird quantum physics is, but how it actually works in the real world. (See, for example, the Wikipedia article, Quantum Entanglement.)

## So... What is light, really?

Despite the fact that we now think that light is "really" made up of photons (whatever they are), that turns out not to be helpful for most of our work with light.

In a similar way, we know that matter is made up of atoms, but for lots of our work in biology, chemistry, and physics, we treat matter as if it's smooth, has well defined properties such as density, viscosity, Young's modulus, thermal conductivity, etc. The graininess of matter means that if we look on too small a scale, our calculation of the density of a gas, for example, will give a different result if our cubic nanometer holds 6 or 7 molecules at a given time. But as long as we don't take too small a scale, we can ignore the fact that matter is "really" made up of atoms.

For light, our "smooth" model of lots of photons usually yields a description of light in terms of Maxwell's electromagnetic waves. For most macroscopic phenomenon, even down to the micron scale, electromagnetic waves is a useful model for light. And physicists can show that the quantum theory of lots of photons actually reduces to Maxwell's equations as a good approximation in most cases.

However, for practical uses at the macro scale — optometry, microscopy, telescopes and binoculars — the wave theory is too cumbersome to work with. Fortunately, in the 19th century, William Rowan Hamilton showed that the wave theory reduced to the ray theory in most cases if the wavelength of the wave could be treated as very short.*

So we are left with a hierarchy of models: the photon theory, the wave theory, and the ray theory. Each in the chain can be imagined to be an approximation of the previous one, and each is useful under the right circumstances.

Since we are interested in how the eye creates images of the world (like in the eye, optometry, or in optical instruments like the microscope), we'll find the ray model of the most value. Since we are interested in powerful observational tools that are useful in biology (like the phase contrast microscope and interferometers) we'll also find the wave model to be useful. But since we also are interested in the interaction of light with atoms and molecules (such as in the absorption of light by rhodopsin in the eye or chlorophyll by plants), we'll also need photons!

So we'll go through the basic principles of each model of light.

— We'll introduce the basic principles of the model, that now seem obvious, thanks to centuries of research. We'll then show how, despite the apparent simplicity of the model, it contains some true results that might surprise you!*The ray model of light*— Building on the tools we developed in studying oscillations and waves on a string, we'll show how the surprising phenomenon of interference happens and how interference patterns can provide the measurement of very small things: like the structure of DNA!**The wave model of light**— The photon model is a mind-bending combination of particle properties (momentum and energy) and waves (wavelength and frequency). But despite the conceptual challenge, it turns out to be reasonably easy to use in many of the relevant cases!*The photon model of light*— Whatever model of light we use, we have to account for the fact that light can be broken up into different colors. This has important implications both for vision and measurement using light.*Color and light*— Once we know the various models of light, we have to consider the various ways that it interacts with matter. While some of this was considered in earlier sections (reflection, refraction), more details play an important role at all scales from the macro to the quantum.*The interaction of light with matter*

Source of currency images: E. Redish, with permission

Joe Redish 7/3/19

* This demonstration played a critical role in Schrödinger's creation of his quantum mechanical wave equation.

Last Modified: August 21, 2020